A stockroom currently has 30 components of a certain type, of which8 were provided by suplier 1, 10 by supplier 2, and 12 by supplier3. Six of these are randomly selected for a particular assembly. Let X = the number of supplier 1's components selected, Y = thenumber of supplier 2's components selected, and p(x, y) denote thejoint pmf of X and Y.

a) What is p(3,2)? [Hint: each sample size 6 is equallylikely to be selected, therefore, p(3,2) = (number of outcomes withX = 3 and Y = 2)/(total number of outcomes).]

b) Using the logic of part a, obtain p9x, y). (This can be thoughtof as a multivariate hypergeometric distribution-sampling withoutreplacement from a finite population consisting of more than 2categories.)